Related papers: Spacetime causality in the study of the Hankel tra…
We are interested in the global solutions to a class of Klein-Gordon equations, and particularly in the unified time decay results with respect to the possibly vanishing mass parameter. We give for the first time a rigorous proof, which…
Klein-Gordon equation is derived for a particle in the brane model of Universe. It is compared with squared Dirac-Fock-Ivanenko equation and expression for a chiral current is obtained by this comparison. This expression defines chiral…
One may ask whether the relations between energy and frequency and between momentum and wave vector, introduced for matter waves by de Broglie, are rigorously valid in the presence of gravity. In this paper, we show this to be true for…
A solution of the sourceless Einstein's equation with an infinite value for the cosmological constant \Lambda is discussed by using Inonu-Wigner contractions of the de Sitter groups and spaces. When \Lambda --> infinity, spacetime becomes a…
We develop causality theory for upper semi-continuous distributions of cones over manifolds generalizing results from mathematical relativity in two directions: non-round cones and non-regular differentiability assumptions. We prove the…
We propose uncertainty relations for the different coordinates of spacetime events, motivated by Heisenberg's principle and by Einstein's theory of classical gravity. A model of Quantum Spacetime is then discussed where the commutation…
In the present paper, we study the Dirac equation in the background of Minkowski space-time on a light cone. With the help of the coupling of the radial parts, the system of 4 equations is reduced to two different second-order differential…
At first we introduce the space-time manifold and we compare some aspects of Riemannian and Lorentzian geometry such as the distance function and the relations between topology and curvature. We then define spinor structures in general…
We study the 1D Klein-Gordon equation with variable coefficient cubic nonlinearity. This problem exhibits a striking resonant interaction between the spatial frequencies of the nonlinear coefficients and the temporal oscillations of the…
Lorentz transformation on two-dimensional spacetime is obtained without assumption of linearity. To obtain this, we use the invariance of wave equations, which is recently proved to be equivalent to the causality preservation.
We construct a class of solutions to the Cauchy problem of the Klein-Gordon equation on any standard static spacetime. Specifically, we have constructed solutions to the Cauchy problem based on any self-adjoint extension (satisfying a…
In the paper the quantum hyperbolic equation formulated in [M. Kozlowski, J. Marciak-Kozlowska, From Quarks to Bulk Matter, Hadronic Press, 2001], is appled to the study of the propagation of the initial thermal state of the Universe. It is…
In quantum physics, disturbance due to a measurement is not negligible. This requires the time parameter $t$ in the Schr\"odinger or Heisenberg equation to be considered differently from a time continuum of experimenter's clock $T$ on which…
The causal relation $K^+$ was introduced by Sorkin and Woolgar to extend the standard causal analysis of $C^2$ spacetimes to those that are only $C^0$. Most of their results also hold true in the case of spacetimes with degeneracies. In…
Weighted discrete Hilbert transforms $(a_n)_n \mapsto \sum_n a_n v_n/(z-\gamma_n)$ from $\ell^2_v$ to a weighted $L^2$ space are studied, with $\Gamma=(\gamma_n)$ a sequence of distinct points in the complex plane and $v=(v_n)$ a…
Vacuum polarization of a massive scalar field in the background of a two-dimensional version of a spinning cosmic string is investigated. It is shown that when the `radius of the universe' is such that spacetime is globally hyperbolic the…
We consider waves, which obey the semilinear Klein-Gordon equation, propagating in the Friedmann-Lemaitre-Robertson-Walker spacetimes. The equations in the de Sitter and Einstein-de Sitter spacetimes are the important particular cases. We…
We investigate the fully general class of non-expanding, non-twisting and shear-free D-dimensional geometries using the invariant form of geodesic deviation equation which describes the relative motion of free test particles. We show that…
We present an elementary proof based on a direct calculation of the property of completeness at constant time of the solutions of the Klein-Gordon equation for a charged particle in a plane wave electromagnetic field. We also review…
The problem of finding null geodesics in a stationary Lorentzian spacetime is known to to be equivalent to finding the geodsics of a Randers-Finlser structure. This latter problem is equivalent to finding the motion of charged particles…